A mathematical function maps each input to exactly one output, with every input and output expressed in its method signature. It produces the same output for a given input on every call. Hidden inputs include internal or external state; hidden outputs include side effects and exceptions. section 6.3 section 6.6
Explicit versus hidden state
Increment(int x) returns x + 1, so its input and output are visible and predictable. An Increment() method that reads and updates an internal x has a hidden input and changes its result across calls. CalculateDiscount(Product[] products) similarly exposes its product input and decimal output. section 6.3
public decimal CalculateDiscount(Product[] products)
{
decimal discount = products.Length * 0.01m;
return Math.Min(discount, 0.2m);
}
CalculateDiscount demonstrates a mathematical function whose product input and discount output are explicit. section 6.3
Explicit inputs and outputs make mathematical functions highly testable because output-based tests remain short, simple, understandable, and maintainable. Functional architecture concentrates such decision-making in a functional core while a mutable shell supplies data and applies side effects. section 6.3 section 6.6
